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  Upper bounds for constant slope p-adic families of modular forms

Bergdall, J. (2019). Upper bounds for constant slope p-adic families of modular forms. Selecta Mathematica, 25(4): 59. doi:10.1007/s00029-019-0505-8.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0005-4334-5 Version Permalink: https://hdl.handle.net/21.11116/0000-0005-52F3-C
Genre: Journal Article
Latex : Upper bounds for constant slope $p$-adic families of modular forms

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Bergdall, John1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Number Theory
 Abstract: We study $p$-adic families of eigenforms for which the $p$-th Hecke eigenvalue $a_p$ has constant $p$-adic valuation ("constant slope families"). We prove two separate upper bounds for the size of such families. The first is in terms of the logarithmic derivative of $a_p$ while the second depends only on the slope of the family. We also investigate the numerical relationship
between our results and the former Gouv\^ea--Mazur conjecture.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: 24
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1708.03663
URI: http://arxiv.org/abs/1708.03663
DOI: 10.1007/s00029-019-0505-8
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Title: Selecta Mathematica
  Abbreviation : Selecta Math.
Source Genre: Journal
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Publ. Info: Cham : Springer
Pages: - Volume / Issue: 25 (4) Sequence Number: 59 Start / End Page: - Identifier: -